Preheat oven to 325°F (165°C). In a large mixing bowl, beat butter and sugars until light and fluffy. Mix in the peanut butter. Add the eggs and vanilla and mix well. With mixer on low speed, mix in the flour, baking soda and salt until combined. Stir in chocolate chips.
Roll dough into golf ball sized balls. Place balls on an ungreased baking sheet and flatten them into thick cookies with your fingers. Bake the cookies for about 10 minutes or until the edges start to brown and the tops form little cracks.
Remove from the oven, allow the cookies to set for a couple of minutes and then transfer them to wire racks to cool completely. Store in an airtight container at room temperature for up to one week or freeze for up to two months.
*Use industrially made peanut butter, not an organic/health-food kind.